Chii is a Chobit, a type of persocom (personal computer) that's more technologically advanced than regular persocoms, and who are said to possess true machine intelligence rather than relying on the execution of pre-loaded software programs like other persocoms.
The name "Chobits" comes from the fact that her creator, Ichiro Mihara, used the word "Chobi" to describe anything he thought was "small and hopelessly adorable". Two Chobi (Chi and her sister Freya) become "Chobits"
She is found by Hideki one night in a pile of trash as he makes his way home from work. He takes her to his apartment and tries to figure out how to activate her. A typical persocom (abbreviated from "personal computer") has its power switch in or behind its ears, but Chi's is located in a very unorthodox place: her crotch. Realizing this, Hideki overcomes his moral objections and manages to activate her. She has difficulty communicating with him at first; the only word that she is able to say being "chi", but slowly she learns how to speak. She is initially fearful that Hideki will discard her because of this, but he reassures her that he would never throw her away. When Hideki decides to give her a name, he remembers the only word that she can say and decides to call her "Chi".
Chi remembers nothing of her past life and is unable to perform simple tasks, so Hideki takes it upon himself to teach her and take care of her. Mimicking Hideki and several other outside round her. She makes many humorous mistakes in the process, including her imitation of a pornographic pose from one of Hideki's magazines, and calling everyone and everything "Hideki" (Hideki had attempted to teach her his name by telling her his name as he pointed at himself, but she believed that he meant that Hideki was what one said when one pointed).
(source; wiki)